First answer:
Jesus didn't institute any sacrament, nor is that word found in The Bible.
Another answer:
The answer you are looking for is the Eucharist.
Jesus (a Jew) instituted the Eucharist the night before he died - Holy Thursday. It was not the Jewish people who instituted it.
If you mean the sacrament of the Lord's Supper, then it was on the night Jesus was betrayed as He and the disciples celebrated the Passover feast.
Christ broke bread and blessed the bread and wine at The Last Supper. He told the Disciples, "Do this in Memory of Me." This was the night before he died.
The Eucharist was instituted by Christ on Holy Thursday: "On the night before he died he had supper with his friends and, taking bread, he praised you. He broke the bread, gave it to them and said: Take, eat; this is my body which is given for you; do this in remembrance of me. When supper was ended he took the cup of wine. Again he praised you, gave it to them and said: Drink this, all of you; this is my blood of the new covenant, which is shed for you and for many for the forgiveness of sins. Do this, as often as you drink it, in remembrance of me." The short phrases above instituted both the Eucharist and the Sacrament of Holy Orders.
Of course you can confess your sins when you pray at night, as a matter of fact, you are urged to do this every night before going to bed. However, do not confuse this with the sacrament of Penance (popularly known as Confession). The Sacrament of Penance (aka Confession) requires a priest.
Jesus spent the whole night in prayer to God, before he chose his apostles. The book of Luke records this.
At the Last Supper, the night before Jesus died.
If you mean the Sacrament 'Holy Orders', it was instituted on the night of the Last Supper, Holy Thursday when Jesus called the Apostles to become the first priests by doing as he did - transforming bread into his body and wine into his blood.
The dream his wife had the night before and her warning against harming Jesus.
Gethsemane is reputed to be the garden at the foot of the Mount of Olives in Jerusalem where, according to the gospels, Jesus and his disciples prayed the night before he was arrested, the day before his death.
He was said to be praying - in the 'Garden of Gethsemane' when he was arrested.
Christmas Eve, December 24, is the night before Christmas Day, which celebrates the birth of Jesus Christ. It is the day to prepare for Christmas.Christams Eve is the night before Christamas Day.